Aldous, D., Miermont, G. & Pitman, J. Probab. Theory Relat. Fields (2005) 133: 1. doi:10.1007/s00440-004-0407-2
We study the asymptotics of the p-mapping model of random mappings on [n] as n gets large, under a large class of asymptotic regimes for the underlying distribution p. We encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees, this exploration process being derived (Aldous-Miermont-Pitman 2004) from a bridge with exchangeable increments. Our setting generalizes previous results by allowing a finite number of “attracting points” to emerge.
Mathematics Subject Classification (2000)
Key words or phrases
Random mappingWeak convergenceInhomogeneous continuum random tree